Most of the polyimides described in the literature are structures containing completely aromatic moieties in the chain. An example of these is "H-film" of Du Pont, which is prepared from pyromellitic bisanhydride and 4,4'-diamino-diphenyl ether. Modifications of such polymers, as for example by the introduction of aliphatic groups and/or alicyclic rings, are known. Such modifications are intended to improve specific properties of the product and to facilitate the processing of these. While some of these known polymers undergo swelling in certain organic solvents, none of these are soluble in organic solvents. All the polyimides described in the literature need a treatment at 300.degree. C to become fully cyclized and thus attain their optimal properties.